Active noise control method and apparatus including feedforward and feedback controllers

ABSTRACT

An active noise control apparatus for reducing noise from a noise source includes a microphone for detecting noise produced by the noise source, and a generalized finite impulse response (FIR) filter for receiving noise signals of the detected noise from the microphone and generating control signals for reducing the noise from the noise source. A speaker produces sound based on the control signals from the generalized FIR filter for substantially canceling the noise from the noise source.

TECHNICAL FIELD

Fields of the invention includes noise cancellation. The inventionconcerns other more particular fields, including but not limited to,active noise control using a feedforward or a feedback controller.

BACKGROUND ART

Sound is an undesired result of many desirable functions. The control ofundesired sound is important in any number of devices. Without somecontrol of sound emitted, for example, by modern devices, many modernenvironments would be largely intolerable to people. Be it thehousehold, the office, the inside of a vehicle, a manufacturing plant,everyday devices produce noise that must be controlled.

One aspect of noise reduction is to make devices and systems thatinherently produce less noise. For example, in computers a solid statememory produces little to no noise when compared to a disk drive.Similarly, an LCD display produces little to no noise when compared to aCRT.

In many instances, however, noise creating features cannot beeliminated. Examples of noise producing devices include motors and fans,both of which are often necessary to provide desirable operations.Similarly, power supplies, transformers, and other device componentsproduce noise. Circulating liquids, in fluid or gas form, also createnoise. Component heating and cooling create noise, such as noise emittedwhen plastic and metal parts cool from high temperature. Accordingly,canceling noise after it is created is often important.

Passive noise cancellation includes sound absorbing materials. These arehighly effective. However, for many reasons, there is an increasedinterest in active noise cancellation. An active noise cancellationsystem may be, in some instances, more efficient and less bulky thanpassive noise cancellation. There remains a need for an improved activenoise cancellation.

Many systems that require noise control exhibit two types ofdisturbances: periodic and non-periodic. Recently, work in the area ofrepetitive control has produced good results in the rejection ofperiodic disturbances. Repetitive controllers can be viewed as anextension of the internal model principle. An internal model, oftencalled a memory loop, is placed in the feedback loop in order to cancelthe repetitive disturbance. Since the standard memory loop is marginallyunstable, it is impractical to implement without modification.Typically, two filters are used to modify the memory loop. One filter isused to create a stable model, and one filter is used to eliminate highfrequency components. This method results in a high order internal modelthat is designed on a trial and error basis. Additionally, non-periodiceffects are often left out of the analysis, and the resulting controllercan over amplify these components.

The invention is directed to methods and systems to address these needs.

DISCLOSURE OF INVENTION

One embodiment of invention uses broadband feedforward soundcompensation, which is a sound reduction technique where a sounddisturbance is measured at an upstream location of the (noisy) soundpropagation and cancelled at a downstream direction of the (noisy) soundpropagation. An active noise control algorithm is the actual computationof a control signal (or compensation signal) that is able to reduce theeffect of an undesired sound source by generating an out-of-phase soundsource. To achieve proper sound cancellation, the active noise controlalgorithm must take into account the dynamic effects of the propagationof both the undesired and the out-of-phase sound source. The inventionprovides such a feedforward noise control algorithm and method that takeinto account the dynamic effects of sound propagation.

The inventive active noise control algorithm described in this inventionuses a FIR (Finite Impulse Response) filter where the orthogonal basisfunctions in the filter are chosen on the basis of the dynamics of thesound propagation. In this approach the standard tapped delay line ofthe FIR filter is replaced by a FIR filter that contains information onhow the sound propagates through the system. The so-called generalizedFIR (GFIR) filter has a much larger dynamic range while maintaining thelinear parameter dependency found in a conventional FIR filter. As aresult, adaptive and recursive estimation techniques can be used toestimate the parameters of the GFIR filter. The GFIR filter requires aninitialization that contains knowledge on sound propagation dynamics.Once actuators and sensors for active noise control have been placed inthe system. The data from the actuators and sensors can be used tomeasure and characterize the dynamics of the sound propagation and thisinformation is used to initialize the GFIR filter.

Another embodiment of the invention concerns a feedback soundcompensation system that treats the affects of both the periodic andnon-periodic noise components. With the present invention, we are ableto design a sound control algorithm that emphasizes the elimination ofperiodic components without over amplifying the non-periodic soundcomponents. The controller is tuned to reject the periodic disturbancesuntil there is no appreciable difference between the periodic andnon-periodic disturbances.

The periodic components are attenuated with the use of an internalmodel. Instead of starting with a standard memory loop and filtering, wedirectly create a stable internal model to shape the controller toreject specific deterministic disturbances. Using known H₂ controltheory, we are able to incorporate periodic and non-periodicdisturbances into the design. In this manner, we are able to design alow order controller that uses an internal model and a stochastic modelto eliminate periodic disturbances in the presence of random noise.

A wide variety of devices and systems in various fields may benefit fromthe invention, e.g., forced air systems, electronic devices, computersystems, manufacturing systems, projectors, etc.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a feedforward active noise control(ANC) system in accordance with one embodiment of the present invention;

FIG. 2 is a block diagram showing a model of the ANC system of FIG. 1;

FIG. 3 is a block diagram of a generalized FIR filter derived from themodel of FIG. 2;

FIG. 4 is a schematic diagram of a feedback active noise control (ANC)system in accordance with one embodiment of the present invention;

FIG. 5 is a graph showing time data of a fan noise;

FIG. 6 is a graph showing the power spectral density of the fan noiseshown in the graph of FIG. 5;

FIG. 7 is a block diagram showing a model for periodic and non-periodicnoise disturbances; and

FIG. 8 is a block diagram showing a model for a controller shown in thefeedback ANC system of FIG. 7.

BEST MODE FOR CARRYING OUT THE INVENTION

Turning now to FIG. 1, an active noise control (ANC) system 10 inaccordance with one embodiment of the present invention includes aninput microphone 12 for measuring noise from an external noise source14, such as fan noise in a forced-air cooling system, for example. The(amplified) signal u(t) from the input microphone 12 is fed into afeedforward compensator (F) 16 that controls the signal u_(c)(t) to acontrol speaker 18 for sound compensation. A signal e(t) from an errormicrophone 20 is used for evaluation of the effectiveness of the ANCsystem 10.

In order to analyze the design of the feedforward compensator 16,consider the block diagram depicted in FIG. 2. Following this blockdiagram, the dynamical relationship between signals in the ANC system 10are characterized by discrete time transfer functions, with qu(t)=u(t+1)indicating a unit step time delay. The spectrum of noise disturbanceu(t) at the input microphone 12 is characterized by filtered white noisesignal n(t) where W(q) 22 is a (unknown) stable and stable invertiblenoise filter. The dynamic relationship between the input u(t) and theerror e(t) microphone signals is characterized by H(q) 24 whereas G(q)26 characterizes the relationship between control speaker signal anderror e(t) microphone signal. Finally, G_(c)(q) 28 is used to indicatethe acoustic coupling from control speaker 18 signal back to the inputu(t) microphone 12 signal that creates a positive feedback loop with thefeedforward F(q). For the analysis, we assume in this that all transferfunctions in FIG. 2 are stable and known. The error microphone signale(t) can be described by $\begin{matrix}{{e(t)} = {{{W(q)}\left\lbrack {{H(q)} + \frac{{G(q)}{F(q)}}{1 - {{G_{c}(q)}{F(q)}}}} \right\rbrack}{n(t)}}} & (1)\end{matrix}$and is a stable transfer function if the positive feedback connection ofF(q) 30 and G_(c)(q) 28 is stable. When the transfer functions in FIG. 2are known, perfect feedforward noise cancellation can be obtained incase $\begin{matrix}{{{F(q)} = {- \frac{H(q)}{{G(q)} - {{H(q)}{G_{c}(q)}}}}}{{{F(q)} = \frac{\overset{\sim}{F}(q)}{1 + {{\overset{\sim}{F}(q)}{G_{c}(q)}}}},{{\overset{\sim}{F}(q)}:={- \frac{H(q)}{G(q)}}}}} & (2)\end{matrix}$and can be implemented as a feedforward compensator 16 in case F(q) 30is a stable and causal transfer function. The expression in equation (2)can be simplified for the situation where the effect of acousticcoupling G_(c) can be neglected. In that case, the feedforwardcompensator 16 can be approximated by $\begin{matrix}{{{F(q)} \approx {\overset{\sim}{F}(q)}} = {- \frac{H(q)}{G(q)}}} & (3)\end{matrix}$and for implementation purposes it would be required that F(q) 30 be acausal and stable filter. In general, the filter F(q) 30 in equation (2)or (3) is not a causal or stable filter due to the dynamics of G(q) 26and H(q) 24 that dictate the solution of the feedforward compensator.Therefore, an optimal approximation has to be made to find the bestcausal and stable feedforward compensator. With equation (1) thevariance of the discrete time error signal e(t) is given by$\frac{\lambda}{2\pi}{\int_{- \pi}^{\pi}{{{W\left( {\mathbb{e}}^{j\omega} \right)}}^{2}{{{H\left( {\mathbb{e}}^{j\omega} \right)} + \frac{{G\left( {\mathbb{e}}^{j\omega} \right)}{F\left( {\mathbb{e}}^{j\omega} \right)}}{1 - {{G_{c}\left( {\mathbb{e}}^{j\omega} \right)}{F\left( {\mathbb{e}}^{j\omega} \right)}}}}}^{2}\quad{\mathbb{d}\omega}}}$where λ denotes the variance of n(t). In case variance minimization ofthe error microphone signal e(t) is required for ANC, the optimalfeedforward controller (F) 16 is found by the minimization$\begin{matrix}{{\min\limits_{\theta}{\int_{\omega = {- \pi}}^{\omega = \pi}{{{L\left( {{\mathbb{e}}^{j\omega},\theta} \right)}}^{2}\quad{\mathbb{d}\omega}}}}:={\min_{\theta}{{{L\left( {q,\theta} \right.}_{2},{{L\left( {q,\theta} \right)} = {{W(q)}\left\lbrack {{H(q)} + \frac{{G(q)}{F\left( {q,\theta} \right)}}{1 - {{G_{c}(q)}{F\left( {q,\theta} \right)}}}} \right\rbrack}}}}}} & (4)\end{matrix}$where the parametrized filter F(q,θ) is required to be a causal andstable filter, in which θ is a real valued parameter determined by theminimization in equation (4).

The minimization in equation (4) can be simplified to${\min\limits_{\theta}{\int_{\omega = {- \pi}}^{\omega = \pi}{{{L\left( {{\mathbb{e}}^{j\omega},\theta} \right)}}^{2}\quad{\mathbb{d}\omega}}}}:={\min_{\theta}{{{L\left( {q,\theta} \right.}_{2},{{L\left( {q,\theta} \right)} = {{W(q)}\left\lbrack {{H(q)} + {{G(q)}{F\left( {q,\theta} \right)}}} \right\rbrack}}}}}$in case the effect of acoustic coupling G_(c) can be neglected. Theminimization in equation (4) is a standard 2-norm based feedback controland model matching problem that can be solved in case the dynamics ofW(q) 22, G(q) 26, H(q) 24 and G_(c)(q) 28 are known.

In case the transfer functions H(q) 24, G(q) 26 and G_(c)(q) 28 arepredetermined, but possibly unknown. It is important to make adistinction between varying dynamics and fixed dynamics in the ANCsystem 10 for estimation and adaptation purposes. An off-lineidentification technique can be used to estimate these transferfunctions to determine the essential dynamics of the feedforwardcontroller. Subsequently, the spectral contents of the sound disturbancecharacterized by the (unknown) stable and stably invertible filter W(q)22 is the only varying component for which adaptation of the feedforwardcontrol is required. Instead of separately estimating the unknowntransfer functions and computing the feedforward controller via anadaptive optimization of equation (4), a direct estimation of thefeedforward compensator 16 can also be performed.

For the analysis of the direct estimation of the feedforward compensator16 we assume that the acoustic coupling G_(c) can be neglected tosimplify the formulae. In that case, the error signal e(t) is given bye(t,θ)=H(q)u(t)+F(q,θ)G(q)u(t)  (5)and definition of the signalsy(t):=H(q)u(t),u _(f)(t):=−G(q)u(t)  (6)leads toe(t,θ)=y(t)−F(q,θ)u _(f)(t)for which the minimization $\begin{matrix}{\min\limits_{\theta}{\frac{1}{N}{\sum\limits_{t = 1}^{N}{e\left( {t,\theta} \right)}}}} & (7)\end{matrix}$to compute the optimal feedforward filter F(q;θ) is a standard outputerror (OE) minimization problem in a prediction error framework. Usingthe fact that the input signal u(t) satisfies ∥u∥₂=|W(q)|²|λ, theminimization of equation (7) for lim _(N→∞) can be rewritten into thefrequency domain expression $\begin{matrix}{\min\limits_{\theta}{\int_{- \pi}^{\pi}{{{W\left( {\mathbb{e}}^{j\omega} \right)}}^{2}{{{H\left( {\mathbb{e}}^{j\omega} \right)} + {{G\left( {\mathbb{e}}^{j\omega} \right)}{F\left( {\mathbb{e}}^{{j\omega},\theta} \right)}}}}^{2}\quad{\mathbb{d}\omega}}}} & (8)\end{matrix}$using Parceval's theorem. Due to the equivalency of equations (8) and(4), the same 2-norm objectives for the computation of the optimalfeedforward compensator are used.

It should be noted that the signals in equation (6) may be obtained byperforming a series of two experiments. The first experiment is donewithout a feedforward compensator 16, making e(t)=H(q)u(t), Δ y(t), ande(t) is the signal measured at the error microphone 20. The input signalu_(f)(t) can be obtained by applying the measured input microphonesignal u(t) from this experiment to the control speaker 18 in a secondexperiment that is done without a sound disturbance. In that situatione(t)=G(q)u(t)Δ−u_(f)(t).

In general, the OE minimization of equation (7) is a non-linearoptimization but reduces to a convex optimization problem in case F(q,θ) is linear in the parameter θ. Linearity in the parameter θ is alsofavorable for on-line recursive estimation of the filter and may beachieved by using a FIR filter parametrization $\begin{matrix}{{{F\left( {q,\theta} \right)} = {\theta_{0} + {\sum\limits_{k = 1}^{N}{\theta_{k}q^{- k}}}}},{\theta = \left\lbrack {\theta_{0},\theta_{1},\ldots\quad,\theta_{N}} \right\rbrack}} & (9)\end{matrix}$for the feedforward compensator F(q,θ). A FIR filter parametrizationalso guarantees the causality and stability of the feedforwardcompensator 16 for implementation purposes.

To improve the approximation properties of the feedforward compensator16 in the ANC system 10, the linear combination of tapped delayfunctions q⁻¹ in the FIR filter of (9) are generalized to$\begin{matrix}{{{F\left( {q,\theta} \right)} = {\theta_{0} + {\sum\limits_{k = 1}^{N}{\theta_{k}{f_{k}(q)}}}}},{\theta = \left\lbrack {\theta_{0},\theta_{1},\ldots\quad,\theta_{N}} \right\rbrack}} & (10)\end{matrix}$where f_(k)(q) are generalized (orthonormal) basis functions that maycontain knowledge on system dynamics, θ₀ is the direct feedthrough termof the generalized FIR filter and θ_(k) are the optimal filtercoefficients of said generalized FIR filter, as described in P. S. C.Heuberger, P. M. J. Van Den Hof, and O. H. Bosgra, “A generalizedorthonormal basis for linear dynamical systems,” IEEE Transactions onAutomatic Control, vol. 40(3), pp. 451-465, 1995, which is incorporatedherein by reference.

The generalized FIR filter can be augmented with standard delayfunctions $\begin{matrix}{{{F(q)} = {q^{- {nk}}\left\lbrack {\theta_{0} + {\sum\limits_{k = 1}^{N}{\theta_{k}{f_{k}(q)}}}} \right\rbrack}},{\theta = \left\lbrack {\theta_{0},\theta_{1},\ldots\quad,\theta_{N}} \right\rbrack}} & (11)\end{matrix}$to incorporate a delay time of n_(k) time steps in the feedforwardcompensator. A block diagram of the generalized FIR filter F(q) 31 inequation (11) is depicted in FIG. 3. It can be seen that it exhibits thesame tapped delay line structure found in a conventional FIR filter,with the difference of more general basis functions f_(k)(q). In thegeneralized FIR filter 31 knowledge of the (desired) dynamical behaviorcan be incorporated in the basis function f_(k)(q). Without anyknowledge of desired dynamic behavior, the trivial choice off_(k)(q)-q⁻¹ reduces the generalized FIR filter 31 to the conventionalFIR filter. If a more elaborate choice for the basis function f_(k)(q)is incorporated, then equation (11) can exhibit better approximationproperties for a much smaller number of parameters N than used in aconventional FIR filter 31. Consequently, the accuracy of the optimalfeedforward controller will substantially increase.

Continuing the line of reasoning described above, where the effect ofthe acoustic coupling G_(c)(q) 28 (shown in FIG. 2) is assumed to benegligible, the parametrization of the generalized FIR filter 31 inequation (11) will be used in the OE minimization of equation (7). Asthe generalized FIR filter 31 is linear in the parameters, convexity ofthe OE minimization is maintained and on-line recursive estimationtechniques can be used to estimate and adapt the feedforward controller16 for ANC purposes. For the construction of the feedforward controller16 based on the generalized FIR filter F(q) 31, we make a distinctionbetween an initialization step and the recursive estimation of thegeneralized FIR filter 31.

To initialize the on-line adaptation of the generalized FIR filter 31,the signals y(t) and u_(f)(t) in equation (6) have to be available toperform the OE-minimization. With no feedforward controller in place,the signal y(t) is readily available viay(t)=H(q)u(t)=e(t)  (12)Because G(q) 26 is fixed once the mechanical and geometrical propertiesof the ANC system in FIG. 2 are fixed, an initial off-line estimationcan be used to estimate a model for G(q) 26 to construct the filteredinput signal u_(f)(t).

Estimation of a model of G(q), indicated by Ĝ(q), can be done byperforming an experiment using the control speaker signal u_(c)(t) (seeFIG. 1) as excitation signal and the error microphone signal e(t) asoutput signal. Construction of the prediction errorε(t,β)=e(t)−G(q,β)u _(c)(t)and a minimization $\begin{matrix}{{{\hat{G}(q)}:={G\left( {q,\hat{\beta}} \right)}},{\hat{\beta} = {\underset{\beta}{argmin}\quad\frac{1}{N}{\sum\limits_{t = 0}^{N}{ɛ^{2}\left( {t,\beta} \right)}}}}} & (13)\end{matrix}$yields a model Ĝ(q) for filtering purposes. Since Ĝ(q) is used forfiltering purposes only, a high order model can be estimated to providean accurate reconstruction of the filtered input signal viaû _(f)(t):=Ĝ(q)u(t)  (14)where û_(f)(t) is a filter version, or model, of the control signalu_(f)(t).

To facilitate the use of the generalized FIR filter 31, a choice is madefor the basis functions f_(k)(q) in equation (10). A low order model forthe basis function will suffice, as the generalized FIR model 31 will beexpanded on the basis of f_(k)(q) to improve the accuracy of thefeedforward compensator 16. As part of the initialization of thefeedforward compensator 16, a low order IIR model {circumflex over(F)}(q) in equation (10) of the feedforward filter F(q) 31 can beestimated with the initial signals available from (12), (14) and theOE-minimization $\begin{matrix}{{{\hat{F}(q)}:={F\left( {q,\hat{\theta}} \right)}},{\hat{\theta} = {\underset{\theta}{argmin}\quad\frac{1}{N}{\sum\limits_{t = 0}^{N}{ɛ^{2}\left( {t,\theta} \right)}}}}} & (15)\end{matrix}$of the prediction errorε(t,θ)=y(t)−F(q,θ)û _(f)(t)where û_(f)(t) is given in equation (14). An input balanced state spacerealization of the low order model {circumflex over (F)}(q) is used toconstruct the basis functions f_(k)(q) in equation (10).

With a known feedforward F(q,θ_(k-1)) already in place, the signal y(t)can be generated viay(t)=H(q)u(t)=e(t)+F(q,θ _(k-1))u _(f)(t)  (16)and requires measurement of the error microphone signal e(t), and thefiltered input signal u_(f)(t)=G(q)u(t) that can be simulated byequation (14). With the signal y(t) in equation (16), û_(f)(t) inequation (14) and the basis function f(q) in equation (10) found by theinitialization in equation (15), a recursive minimization of thefeedforward filter is done via a standard recursive least squaresminimization $\begin{matrix}{\theta_{k} = {\underset{\theta}{argmin}\frac{1}{k}{\sum\limits_{t = 0}^{k}{{\lambda(t)}\left\lbrack {{y(t)} - {{F\left( {q,\theta} \right)}\quad{{\hat{u}}_{f}(t)}}} \right\rbrack}^{2}}}} & (17)\end{matrix}$where F(q, θ) is parametrized according to equation (11) and λ(t)indicates an exponential forgetting factor on the data. As thefeedforward compensator or controller 16 is based on the generalized FIRmodel 31, the input û_(f)(t) is also filtered by the tapped delay lineof basis functions. Since the filter is linear in the parameters,recursive computational techniques can be used to update the parameterθ_(k).

In the implementation of feedforward based active noise control (ANC)system 10, design freedom for the location of the input microphone 12should be exploited to enhance the performance of the ANC system. Theperformance can be improved by 1: minimize coupling between controlspeaker 18 and input microphone 12, also known as acoustic coupling and2: maximize the effect of the feedforward filter 16 for active noisecontrol.

In order to study these two effects on the performance of the ANC system10, consider a certain location of the input microphone in the ANCsystem 10. For that specific location, the transfer functions H(q), G(q)in equation (3) are fixed, but unknown. As a result, the performance ofthe ANC system 10 solely depends on the design freedom in thefeedforward compensator F(q, θ) 31 to minimize the error signal e(t, θ)in equation (5). The ability to minimize the error signal e(t, θ) isrestricted by the parametrization of F(q, θ) and an optimization of thefeedforward filter F(q, θ) can be performed by considering theparametrized error signal e(t, θ) in terms of the signalsy(t):=H(q)u(t),u_(f)(t):=−G(q)u(t) in equation (6). For a specificlocation of the input microphone 12, the signals in (6) are easilyobtained by performing a series of two experiments. The two experimentsmeasure the input and error microphone signals u(t) and e(t).

The first experiment is done without feedforward compensation. HenceF(q, θ)=0 and the error microphone signal satisfiese ₁(t)=H(q)u(t)  (18)In addition, the input microphone 12.ũ(t)=u(t)+v(t)  (19)is measured, where v(t) indicates possible measurement noise on theinput microphone signal u(t). This results in additional disturbances onthe input microphone signal u(t) that need to be considered in theoptimal location of the microphone 12.

The second experiment is done with the noise source 14 turned off,eliminating the presence of the external sound disturbance.Subsequently, the measured input microphone signal −ũ(t) given inequation (19) from the first experiment is applied to the controlspeaker 18, yielding the error microphone signale ₂ (t)=−G(q)ũ(t)=−G(q)u(t)−G(q)v(t)  (20)With u_(f)(t):=−G(q) u(t), the error microphone signal e(t, θ) can bewritten ase(t,θ)=e ₁(t)−F(q,θ)e ₂(t)−F(q,θ)G(q)v(t)  (21)

Alternatively, both experiments can be combined by using a filteredinput signal u_(f)(t) that is based on an estimated model Ĝ(q) of G(q).Because G(q) is fixed once the location of the control speaker 18 isdetermined, an initial off-line estimation can be used to estimate amodel for G(q) to construct the filtered input signal u_(f)(t).

In the absence of the noise v(t) on the input microphone 12, theminimization of e(θ) in (21) is equivalent to the minimization of e(t,θ) in (6). As a result, the obtainable performance of the ANC 10 systemfor a specific location of the input microphone 12 can be evaluateddirectly on the basis of the error microphone signals e₁(t) and e₂(t) asdefined in equation (18) and (20) and obtained from the first and secondexperiment as defined above. The result is summarized in the followingproposition.Proposition 1. The performance of the feedforward ANC system 10 for aspecific location of the input microphone 12 is characterized byv_(N)({circumflex over (θ)}). The numerical value of v_(N)({circumflexover (θ)}) is found by measuring e₁(t) and e₂(t) for t=1, . . . ,N asdescribed by the experiments above, and solving an OE model estimationproblem $\begin{matrix}{{\hat{\theta} = {\underset{\theta \in R^{d}}{{argmin}\quad}{V_{N}(\theta)}}},{with}} \\{{V_{N}(\theta)}:={\frac{1}{N}{\sum\limits_{t = 1}^{N}{ɛ^{2}\left( {t,\theta} \right)}}}} \\{{ɛ\left( {t,\theta} \right)}:={{e_{1}(t)} - {{F\left( {q,\theta} \right)}\quad{e_{2}(t)}}}}\end{matrix}$for a finite size d parameter θεR^(d) that represents the coefficientsof a finite order filter F(q, θ).

A finite number d of filter coefficients is chosen in Proposition 1 toprovide a feasible optimization of the filter coefficients. It should benoted that an FIR parametrization${{F\left( {q,\theta} \right)} = {\theta_{0} + {\sum\limits_{k = 1}^{d}{\theta_{k}q^{- k}}}}},{\theta = \left\lbrack {\theta_{0},\theta_{1},\ldots\quad,\theta_{d}} \right\rbrack}$leads to an affine optimization of the filter coefficients. Although FIRfilter representations (i.e., equation (9)) require many filtercoefficients θ_(k) for an accurate design of a feedforward filter, theFIR filter is used only to evaluate the possible performance of the ANCsystem 10 for a specific input microphone 12 location. For the actualANC system 10 the feedforward filter is replaced by the generalized FIRfilter as presented above.

In accordance with another embodiment of the present invention, anactive noise control (ANC) system includes a feedback system that treatsthe affects of both the periodic and non-periodic noise disturbances.With the present system we are able to design a controller thatemphasizes the elimination of periodic components without overamplifying the non-periodic components using an additional feedbackcontrol algorithm. The controller is tuned to reject the periodicdisturbances until there is no appreciable difference between theperiodic and non-periodic disturbances.

Turning to FIG. 4, a feedback ANC system 32 in accordance with oneembodiments includes a microphone 34 for measuring noise from a noisesource 36, such as, for example, a server cooling fan; a speaker 38 forgenerating appropriate signal to cancel unwanted periodic noise from thenoise source 36; and a mount 40 for holding the microphone 34 and thespeaker 38 proximate the noise source 36. A controller 42 is providedfor controlling the output of the speaker 38 based on the noise measuredby the microphone 34.

The speaker 38 and the microphone 34 are positioned inside of the mount40, which may be a polyurethane acoustical foam and acrylic, and isorientated so that the sound from the noise source 36 propagates towardsthe microphone 34. It should be noted that the speaker 38 and themicrophone 34 are very close together and are mounted proximate to anddownstream of the noise source 36.

The noise due to the noise source 36 such as, for example, a servercooling fan, as measured by the microphone 34, is shown in FIGS. 5 and6. FIG. 5 shows the time data of the fan noise, and FIG. 6 shows thepower spectral density. There are two distinct types of disturbances.One is periodic; the peaks at evenly spaced frequencies are harmonics ofthe fan (approximately every 1000 Hz, for example). The other isnon-periodic noise due to turbulence, vibrations, and the actualnon-periodic noise of the fan. The effect of wind and vibrations can bemodeled as filtered white noise in the measurement.

The design method for the active noise feedback control algorithm forthe controller 42 in accordance with an embodiment of the inventiondivides the source noise into two distinct disturbances: periodic andnon-periodic. The present method helps lower the order of the controller42 and simplifies the disturbance modeling. FIG. 7 shows how bothdisturbances are modeled, where H_(n)(q) 44 is the non-periodicdisturbance model, H_(p)(q) 46 is the periodic disturbance model, andG(q) 48 is the dynamic feedback relation between feedback controlspeaker 38 and feedback control microphone 34 and defined as “the plant”in the following. In FIG. 7 the signal u(t) is the signal send to thefeedback control speaker 38 and y(t) is the signal measured by thefeedback control microphone 34. The signal v_(n)(t) models thenon-periodic noise component of the sound as a filtered white noisesignal e(t) and v_(p)(t) models the periodic noise component of thesound.

The non-periodic or random disturbances are modeled as colored noise.That is, v_(n)(t) is a random process that is driven by white noise e(t)that is filtered by H_(n)(q) 44, where q is the time shift operator. Theperiodic disturbances are modeled as a standard memory loop H_(p)(q) 46with an unknown initial condition x₀. When added together, v_(n)(t) andv_(p)(t) produce the same result as a single disturbance model.

In one embodiment of the invention, the disturbance model shown in FIG.7 is modified, as shown in FIG. 8, to design the optimal controlalgorithm for the reduction of periodic noise disturbances. The signalz₁(t) and z₂(t) are used to measure the performance of the feedback ANC32 system, where α can be used to specify the relative weighting betweenthe performance signals z₁(t) and z₂(t). The optimal control algorithmK(q) 50 minimizes the H₂ norm of the transfer function matrix betweene(t) and (z₁(t) z₂(t)). The signals e(t) and (z₁(t) z₂(t)) are chosen sothat the control energy and output will be minimized by the optimalfeedback control algorithm K(q) 50. To account for the periodicdisturbances that need to be cancelled, an internal model representationW_(i)(q) 52 is placed in the path from e(t) to y(t) so that theresulting controller will have the general shape of the internal model.Substantially perfect cancellation of all periodic noise componentscould be achieved by choosing W_(i)(q)=H_(p)(q) (shown in FIG. 8) butthe presence of such an internal model in the feedback control algorithmmay cause instabilities of the feedback ANC system 32. The main purposeof W_(i)(q) 52 is to model only those period components in the noisefilter H_(p)(q) 46 for which periodic noise disturbance rejection isdesired. This makes the control algorithm less complex and stability ofthe feedback ANC system 32 can be satisfied much easier. Subsequently,the optimal design of the feedback control algorithm is solved bysolving the minimization: $\begin{matrix}{{K(q)} = {\underset{K}{argmin}\quad{\begin{matrix}\frac{\alpha\quad{W_{i}(q)}{K(q)}{H_{n}(q)}}{1 - {{G(q)}{W_{i}(q)}{K(q)}}} \\\frac{{W_{i}(q)}{H_{n}(q)}}{1 - {{G(q)}{W_{i}(q)}{K(q)}}}\end{matrix}}_{2}}} & (22)\end{matrix}$In the minimization of equation (22), a feedback control algorithm iscomputed that will not invert the effect of the internal model W_(i)(q)52. As a result, the combined active noise feedback control algorithmK(q)W_(i)(q) will have the general shape of W_(i)(q) and eliminate theperiodic disturbances in the noise components.

While specific embodiments of the present invention have been shown anddescribed, it should be understood that other modifications,substitutions and alternatives are apparent to one of ordinary skill inthe art. Such modifications, substitutions and alternatives can be madewithout departing from the spirit and scope of the invention, whichshould be determined from the appended claims.

Various features of the invention are set forth in the appended claims.

1. An active noise control apparatus for reducing noise from a noisesource, comprising: a first detector for detecting noise produced by thenoise source; a generalized finite impulse response (FIR) filter forreceiving noise signals of the detected noise from said first detector,and generating control signals for reducing the noise from the noisesource; and a sound generator for producing sound based on said controlsignals from said generalized FIR filter for substantially canceling thenoise from the noise source.
 2. The apparatus as defined in claim 1wherein said generalized FIR filter is a feedforward compensator.
 3. Theapparatus as defined in claim 2, wherein said first detector is locateddownstream of the noise source, and said sound generator is locateddownstream of said first detector.
 4. The apparatus as defined in claim1 wherein said generalized FIR filter is described by${{F\left( {q,\theta} \right)} = {\theta_{0} + {\sum\limits_{k = 1}^{N}{\theta_{k}{f_{k}(q)}}}}},{\theta = \left\lbrack {\theta_{0},\theta_{1},\ldots\quad,\theta_{N}} \right\rbrack}$where f_(k)(q) are generalized (orthonormal) basis functions includinginformation on a desired dynamic behavior of said generalized FIRfilter, θ₀ is the direct feedthrough term of said generalized FIR filterand θ_(k) are optimal filter coefficients of said generalized FIRfilter.
 5. The apparatus as defined in claim 4, wherein said generalizedFIR filter is constructed by initializing said basis function f_(k)(q),and recursively estimating said θ_(k) based on said initialized basisfunctions f_(k)(q).
 6. The apparatus as defined in claim 5, wherein saidbasis function f_(k)(q) are initialized by a predetermined dynamicalmodel that includes initial approximate information dynamics of saidgeneralized FIR filter.
 7. The apparatus as defined in claim 5, whereinsaid parameters θ_(k) are recursively estimated by a recursiveLeast-Squares optimization routine.
 8. The apparatus as defined in claim1 further comprising a second detector for detecting noise downstream ofsaid sound generator.
 9. The apparatus as defined in claim 8, wherein asignal of the noise detected by the second detector is described by${e(t)} = {{{W(q)}\left\lbrack {{H(q)} + \frac{{G(q)}{F(q)}}{1 - {{G_{c}(q)}{F(q)}}}} \right\rbrack}{n(t)}}$where, W(q) is a stable and stable invertible noise filter for a whitenoise signal n(t); H(q) characterizes a dynamic relationship between theinput signal u(t) from said first detector and said signal e(t) detectedby said second detector; G(q) characterizes the relationship betweensaid control signal from said generalized FIR filter F(q) and saidsignal e(t) detected by said second detector; and G_(c)(q) indicates anacoustic coupling from said sound generator signal back to said signalu(t) from said first detector that creates a positive feedback loop withsaid generalized FIR filter F(q).
 10. The apparatus as defined in claim9, wherein said first detector is located based on conditions at thesecond detector which satisfye ₁(t)=H(q)u(t) ande ₂(t)=−G(q)ũ(t)=−G(q)u(t)−G(q)v(t) where v(t) indicates a disturbancedetected by said first detector.
 11. The apparatus as defined in claim1, wherein said first detector and said second detector are microphones,and said sound generator is a speaker.
 12. A method for reducing noisefrom a noise source in an active noise control system, comprising:detecting first noise produced by the noise source; generating controlsignals from a generalized finite impulse response (FIR) filter forreducing the first noise from the noise source based on a first signalof said detected noise; and producing sound based on said controlsignals for substantially canceling said first noise from the noisesource.
 13. The method as defined in claim 12 wherein said generalizedFIR filter is a feedforward compensator.
 14. The method as defined inclaim 13, wherein said first noise is detected by a microphone locateddownstream of the noise source, and said sound is produced by a speakerlocated downstream of said microphone.
 15. The method as defined inclaim 12 wherein said generalized FIR filter is described by${{F\left( {q,\theta} \right)} = {\theta_{0} + {\sum\limits_{k = 1}^{N}{\theta_{k}{f_{k}(q)}}}}},{\theta = \left\lbrack {\theta_{0},\theta_{1},\ldots\quad,\theta_{N}} \right\rbrack}$where f_(k)(q) are generalized (orthonormal) basis functions containinginformation on a desired dynamic behavior of said generalized FIRfilter, θ₀ is a direct feedthrough term of said generalized FIR filterand θ_(k) are optimal filter coefficients of said generalized FIRfilter.
 16. The method as defined in claim 15, wherein said generalizedFIR filter is constructed by initializing said basis function f_(k)(q),and recursively estimating said θ_(k) based on said initialized basisfunction f_(k)(q).
 17. The method as defined in claim 16, wherein saidbasis function f_(k)(q) is initialized by a predetermined dynamicalmodel that includes initial approximate information dynamics of saidgeneralized FIR filter.
 18. The method as defined in claim 16, whereinsaid θ_(k) are recursively estimated by a recursive Least-Squaresoptimization routine.
 19. The method as defined in claim 12 furthercomprising detecting second noise after said sound based on said controlsignals has been produced.
 20. The method as defined in claim 19,wherein a second signal of the noise detected after said sound based onsaid control signals has been produced by the second detector isdescribed by${e(t)} = {{{W(q)}\left\lbrack {{H(q)} + \frac{{G(q)}{F(q)}}{1 - {{G_{c}(q)}{F(q)}}}} \right\rbrack}{n(t)}}$where, W(q) is a stable and stable invertible noise filter for a whitenoise signal n(t); H(q) characterizes a dynamic relationship between thefirst signal u(t) said second signal e(t); G(q) characterizes therelationship between said control signal from said generalized FR filterF(q) and said first signal e(t); and G_(c)(q) indicates an acousticcoupling from said sound generator signal back to said first signal u(t)that creates a positive feedback loop with said generalized FIR filterF(q).
 21. The method as defined in claim 20, wherein said first noise isdetected at a location based on conditions which satisfye ₁(t)=H(q)_(u)(t) ande ₂(t)=−G(q)ũ(t)=−G(q)u(t)−G(q)v(t) where v(t) indicates a third noisedetected along with said first noise.
 22. An active noise controlapparatus for reducing periodic noise from a noise source, comprising: adetector for detecting noise produced by the noise-source; a controllerfor generating control signals for compensating the periodic noisedetected in the noise; and a sound generator for producing sound basedon said control signals from said controller for substantially cancelingthe periodic noise from the noise source; wherein said control signal isgenerated based on an equation,${K(q)} = {\arg\quad{\min\limits_{K}{\begin{matrix}\frac{\alpha\quad{W_{i}(q)}{K(q)}{H_{n}(q)}}{1 - {{G(q)}{W_{i}(q)}{K(q)}}} \\\frac{{W_{i\quad}(q)}{H_{n}(q)}}{1 - {{G(q)}{W_{i}(q)}{K(q)}}}\end{matrix}}_{2}}}$ where, W_(i)(q) is a discrete time internaldynamical model for reducing periodic disturbances, H_(n)(q) is adiscrete time filter used to model the spectrum of the non-periodicnoise disturbances, G(q) is a discrete time filter that models thedynamics between sound generator and said detector and α is a scalarreal-valued constant.
 23. The apparatus as defined in claim 22, whereinsaid controller comprises a feedback controller.
 24. The apparatus asdefined in claim 22, wherein said detector is a microphone and saidsound generator is a speaker, said microphone and said speaker beingpositioned proximate and downstream of the noise source.
 25. A methodfor reducing periodic noise from a noise source, comprising: detectingnoise produced by the noise source; generating control signals from acontroller for compensating the periodic noise detected in the noise;and producing sound based on said control signals from said controllerfor substantially canceling the periodic noise from the noise source;wherein said control signal is generated based on an equation,${K(q)} = {\arg\quad{\min\limits_{K}{\begin{matrix}\frac{\alpha\quad{W_{i}(q)}{K(q)}{H_{n}(q)}}{1 - {{G(q)}{W_{i}(q)}{K(q)}}} \\\frac{{W_{i\quad}(q)}{H_{n}(q)}}{1 - {{G(q)}{W_{i}(q)}{K(q)}}}\end{matrix}}_{2}}}$ where, W_(i)(q) is a discrete time internaldynamical model for reducing periodic disturbances, H_(n)(q) is adiscrete time filter used to model a spectrum of the non-periodic noisedisturbances, G(q) is a discrete time filter that models the dynamicsbetween a sound generator for producing said sound based on said controlsignals and a detector for detecting the noise produced by the noisesource, and α is a scalar real-valued constant.
 26. The method asdefined in claim 25, wherein said controller comprises a feedbackcontroller.
 27. The method as defined in claim 25, wherein the noise isdetected by a microphone and said sound based on said control signalsfrom said controller is produced by a speaker, said microphone and saidspeaker being positioned proximate and downstream of the noise source.